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Energy dissipation rates, eddy diffusivity, and the Prandtl number: An in situ experimental approach and its consequences on radar estimate of turbulent parameters

Abstract : Different methods have been proposed to derive the energy dissipation rate and eddy diffusion coefficients from ST radar measurements. However, their validity is still questionable because they implicitly assume that the Prandtl number is always equal to one, an assumption which is not verified. An experimental approach to this question, using balloon-borne experiment results, is proposed in this paper in order to test the validity/invalidity of the methods generally used. In situ observations show mat the potential temperature gradient is more efficiently (and probably more rapidly) eroded by the turbulent activity than the wind shear. As a consequence of this observational evidence already mentioned by Browning and Watkins [1970], the structure function constant for temperature fluctuations (C T 2 ) is vanishing within fully developed turbulent layers and exibits maxima on their boundaries, while the structure parameter for wind fluctuations (C V 2 ) presents a broad maximum within the same layer and is decreasing at its boundaries. Consequently, the gradient Richardson number R i strongly varies within fully developed turbulent layers, from R i close to zero (near their center) up to R i > 1 (at their boundaries). By contrast, the flux Richardson number R f , which describes the evolution of the ratio between buoyancy flux and turbulent energy production, remains apparently quasi-constant and close to its critical value during the erosion processes, so that the Prandtl number is not a constant close to unity but might also strongly vary during the turbulent life cycle. These results are in good agreement with laboratory experiments in statistically stable fluids reviewed by Thorpe [1973] and with experimental results obtained in the boundary layer [Businger et al., 1971; Gossard and Frisch, 1987]. ST radar are generally not able to observe regions where the potential temperature gradient is eroded by the turbulent activity but may obtain strong responses on the boundaries of fully developed turbulent layers. This behavior does not affect the radar capability of estimating eddy dissipation rate ε and eddy diffusivity K θ (or K M ) when complementary information on temperature profiles and humidity are available. It is shown that the “nonlocal” mean potential temperature gradient, the wind shear, and the flux Richardson number are the pertinent parameters allowing a correct estimate of the eddy dissipation rates and eddy diffusion coefficients, from C n 2 (C T 2 ) and rms turbulent vertical wind, in regions where the turbulent activity is observable by ST radars.
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François Bertin, Jean Barat, Richard Wilson. Energy dissipation rates, eddy diffusivity, and the Prandtl number: An in situ experimental approach and its consequences on radar estimate of turbulent parameters. Radio Science, American Geophysical Union, 1997, 32 (2), pp.791-804. ⟨10.1029/96RS03691⟩. ⟨insu-03580868⟩

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